In 2019, Jost and Mulas [1]} introduced chemical hypergraphs with the aim of modelling chemical reaction networks. They also introduced two normalized Laplace operators for chemical hypergraphs, the vertex Laplacian \(L\)  and the hyperedge Laplacian \(L^H\) , as a generalization of the classical theory introduced by Chung for graphs. We have noticed that \(L\)  is not necessarily a symmetric matrix, but it is a symmetric operator with respect to the scalar product that we use. Similarly, Reff and Rusnak [2]} introduced signed hypergraphs, that is, a hypergraph where each vertex-edge incidence is given a label of \(+1\)  or \(-1\) . Shi [3]} called this type of hypergraph a signed hypergraph and used it to model the constrained via minimization (CVM) problem or two-layer routings. Such structure allows modeling many real networks, as for instance chemical reaction networks, metabolic networks, neural networks, synchronization networks. A consequence of studying signed hypergraphs is that graphs and signed graphs can be viewed as specializations. A graph can be thought of as a signed hypergraph where each edge is contained in two incidences, and exactly one incidence of each edge is signed \(+1\) . A signed graph can be thought of as a signed hypergraph where each edge is contained in two incidences. Mulas and Zhang [4]} shown some new spectral properties of the normalized Laplacian defined for signed hypergraphs, and obtained the signless nodal domain theorem for the normalized Laplacian of the signed hypergraphs.
